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Enriched categories, topoi, abelian categories, monoidal categories, homological algebra.

5 votes
1 answer
212 views

Is there a name for this variant of the category of elements of a profunctor?

Let $\mathsf{C}$ be a category and let $P : \mathsf{C}^{\text{op}} \times \mathsf{C} \to \mathsf{Set}$ be a functor. Let $\mathsf{E}$ be the category whose: objects are pairs $(X,x)$, where $X$ is an …
diracdeltafunk's user avatar
16 votes

Are functor categories with triangulated codomains themselves triangulated?

I believe I have a simpler counterexample, which I learned from Paul Balmer's course on tensor-triangular geometry last spring: Claim The arrow category $\mathcal{T}^{\bullet \to \bullet}$ of a triang …
diracdeltafunk's user avatar